Method for transmitting symbols through at least a communication channel

ABSTRACT

The present invention concerns a method for transmitting symbols through at least a channel in a telecommunication system including at least one transmitter ( 10 ) provided with at least two transmitting antennas (Antt  1 , Antt  2 ) and at least one receiver provided with at least one receiving antenna (Antr  1 ), the method includes an encoding step wherein a vector comprising symbols is multiplied by a coding matrix for producing coded symbols to be transmitted over the at least one communication channel established between the transmitter ( 10 ) and the receiver ( 20 ), wherein the coding matrix is calculated from an eigenvalue decomposition of a matrix obtained by calculating at least the Kronecker product of the identity matrix of size N, N being the time and/or the frequency dimension of the code and a matrix obtained from an estimated correlation matrix of the response of the channel. The invention concerns also the associated device and a method and device for decoding symbols.

The present invention relates to a method for transmitting symbolsthrough at least a communication channel in a telecommunication systemincluding at least one transmitter provided with at least twotransmitting antennas and at least one receiver provided with at leastone receiving antenna, which method includes an encoding step whereinvectors comprising symbols are multiplied by a coding matrix forproducing symbols to be transmitted over the at least one communicationchannel established between the transmitter and the receiver.

More precisely, the present invention is particularly adapted when thetransmitter has not a precise knowledge of the communication channelsand when the receiver is a Minimum Mean Square Error (MMSE) receiverwhich has a very good knowledge of the communication channels.

Telecommunication systems in which a plurality of antennas are used at areceiver end and/or at a transmitter end of a wireless link, are calledMultiple Input Multiple Output systems (further referred to as MIMOsystems). MIMO systems have been shown to offer large transmissioncapacities compared to those offered by single antenna systems. Inparticular, MIMO capacity increases linearly with the number oftransmitting or receiving antennas, whichever the smallest, for a givenSignal-to-Noise Ratio and under favourable uncorrelated channelconditions. Such MIMO techniques can be combined with multi-carriermodulation techniques based on OFDM (standing for Orthogonal FrequencyDivision Multiplex), whose use in future wireless systems is alsoconsidered.

Dedicated coding has been investigated over the past years to properlyexploit the possibilities of MIMO. These coding schemes generally spanboth the space dimension and the time dimension, hence their name ofSpace Time Codes (ST Codes). They may alternatively span also thefrequency dimension eg. several subcarriers in an OFDM system, and arethen called Space-Time Frequency Codes (STF Codes).

According to the invention, a STF code is a coding scheme which spansthe space and time and/or frequency dimensions. An STF code can be acoding scheme which spans the space and time dimensions or a codingscheme which spans the space and frequency dimensions or a coding schemewhich spans the space and time and frequency dimensions.

The purpose of these coding schemes is to use the spatial dimension ofMIMO with good performance. The spatial dimension can be used toincrease the data rate at a given error rate performance. This isachieved through spatial multiplexing as it is disclosed in the paper ofG. D. Golden, G. J. Foschini, R. A. Valenzuela, P. W. Wolniansky,entitled “Detection Algorithm and Initial Laboratory Results using theV-BLAST Space-Time Communication Architecture”, published in ElectronicsLetters, Vol. 35, No. 1, Jan. 7, 1999, pp. 14-15.

The spatial dimension can also be used to improve the error rateperformance at a fixed data rate. As example, codes exploit the transmitand receive antennas diversity as it is disclosed in the paper of S. M.Alamouti, entitled “A simple transmitter diversity scheme for wirelesscommunications” published in IEEE J. Selected Areas in Communications,vol. 16, pp. 1451-1458, October 1998.

From a general point of view, STF codes are used to address a variety ofcases combining these two possibilities of spatial multiplexing andperformance improvement through space diversity.

The most popular type of STF codes referred as space time block codes,as opposed to space-time trellis codes, are represented with concisematrix notations, where the number of possible codewords depends on thematrix size. These codes are ideally decoded by exhaustive search likeMaximum Likelihood (ML) decoding, or A Posteriori Probability (APP)decoding, or approximations of it, such as sphere decoding and listsphere decoding.

Especially, they are designed assuming such type of ideal receivers. Themain issue is that the decoder complexity is very large as it isexponential with the input size in the case of ML or APP decoding, andpolynomial with the input size in the case of sphere decoding or listsphere decoding, which makes their implementation in a mobile receiverdifficult to realize, especially at high spectral efficiencies.

On the contrary, MMSE decoding, which is a generic well known type ofdecoding, has rather low complexity. It is a very good candidate for apractical implementation.

Besides, the existing STF block codes are generally designed assumingperfect transmit de-correlation, which is neither the case in realitywhere residual correlation exists between the transmit antennas on oneside and receive antenna or antennas on the other side. The residualcorrelation is due to the antennas collocation and due to propagationconditions.

The present invention proposes a STF Code design or a STF pre-codingdesign under more realistic assumptions of residual and known transmitcorrelation and assuming the use of MMSE decoder at the receiver side.

To that end, the present invention concerns a method for transmittingsymbols through at least a channel in a telecommunication systemincluding at least one transmitter provided with at least twotransmitting antennas and at least one receiver provided with at leastone receiving antenna, the method includes an encoding step wherein avector comprising symbols is multiplied by a coding matrix for producingcoded symbols to be transmitted over the at least one communicationchannel established between the transmitter and the receiver,characterised in that the coding matrix is calculated from an eigenvaluedecomposition of a matrix obtained by calculating at least the Kroneckerproduct of the identity matrix of size N, N being the time and/or thefrequency dimension of the code and a matrix obtained from an estimatedcorrelation matrix of the response of the channel.

According to still another aspect, the present invention concerns adevice for transmitting symbols through at least a channel in atelecommunication system including at least one transmitter providedwith at least two transmitting antenna and at least one receiverprovided with at least one receiving antennas, the device comprisingencoding means wherein a vector comprising symbols is multiplied by acoding matrix for producing coded symbols to be transmitted over the atleast one communication channel established between the transmitter andthe receiver, characterised in that the device comprises means forcalculating the coding matrix from an eigenvalue decomposition of amatrix obtained by calculating at least the Kronecker product of theidentity matrix of size N, N being the time and/or the frequencydimension of the code and a matrix obtained from an estimatedcorrelation matrix of the response of the channel.

Thus, through the Kronecker product, the time and/or frequency dimensionis included in the channel description. It has space and a time and/or afrequency dimension, which allows to design codes considering jointlythese three dimensions or part of these dimensions.

According to a first aspect of the present invention, the coding matrix{tilde over (C)} is a real matrix calculated from an eigenvaluedecomposition of a matrix {tilde over (R)}_(TX)* being obtained bycalculating the Kronecker product of the identity matrix I_(N) of size Nand the real part R_(TX) ^(R) of the estimated transmit correlationmatrix of the response of the channel and by calculating the Kroneckerproduct of the identity matrix I_(N) of size N and the imaginary partR_(TX) ^(I) of the estimated transmit correlation matrix of the responseof the channel.

Thus, through the Kronecker product, the time and/or frequency dimensionis included in the channel description, so that the coding solution is aSTF code.

According to a particular feature, the matrix {tilde over (R)}_(TX)* isequal to.

${{\overset{\sim}{R}}_{Tx}^{*} = \begin{pmatrix}{I_{N} \otimes R_{Tx}^{R}} & {I_{N} \otimes R_{Tx}^{I}} \\{{- I_{N}} \otimes R_{Tx}^{I}} & {I_{N} \otimes R_{Tx}^{R}}\end{pmatrix}},$wherein

is the Kronecker product.

According to a particular feature, the eigenvalue decomposition of thematrix {tilde over (R)}_(TX)* is equal to Ũ{tilde over (Λ)}Ũ′, wherein Ũis the matrix of the eigenvectors of the matrix {tilde over (R)}_(TX)*,Ũ′ is the transpose of the matrix Ũ and {tilde over (Λ)} is a diagonalnon negative matrix comprising the eigenvalues of the matrix {tilde over(R)}_(TX)*, and in that the coding matrix {tilde over (C)} is obtainedby multiplying a matrix Ũ′ formed by a part of the columns of the matrixŨ by a diagonal matrix {tilde over (Λ)}′ formed by a part of thediagonal matrix {tilde over (Λ)}.

Thus, the performances are improved.

According to a particular feature, the matrix {tilde over (Λ)}′ isformed by selecting the 2*Q largest non zero diagonal values of thematrix {tilde over (Λ)}, wherein Q is the number of symbols comprisedwithin the vector comprising symbols and the matrix Ũ′ comprises the 2*Qcolumns of the matrix Ũ associated, in the same order, with the 2*Qlargest values selected for the matrix {tilde over (Λ)}′.

Thus, the performances are improved.

According to a particular feature, the number Q of symbols comprisedwithin the vector comprising symbols is not divisible by the dimensionN.

According to a particular feature, the coding matrix {tilde over (C)} iscalculated from a third matrix V′^(t), the matrix V′^(t) being thetranspose of an orthonormal matrix V′ of dimension 2*Q.

According to a particular feature, the matrix V′ is obtained from aDiscrete Fourier Transform matrix or the matrix V′ is an Hadamard matrixof dimension 2*Q when 2*Q is a power of two.

It has to be noted here that, a matrix of dimension Q or 2Q should beunderstood as a square matrix of dimension Q by Q or 2*Q by 2*Q.

According to a particular feature, the coding matrix {tilde over (C)} iscalculated using the following formula:{tilde over (C)}=βŨ′{tilde over (Λ)}′ ^(−1/4) V′ ^(t)

wherein β=√{square root over (P/Tr({tilde over (Λ)}′^(−1/2)))} for apredetermined average transmit power of P.

According to a second aspect of the present invention, the coding matrixis a STF linear pre-coding matrix C_(c) obtained from R*_(TX), which isthe conjugate matrix of the estimated transmit correlation matrix R_(TX)of the frequency response of the channel.

Thus, through the Kronecker product, the time and/or frequency dimensionis included in the channel description.

According to a particular feature, the eigenvalue decomposition of thematrix I_(N)

R_(TX)* is equal to UΛU^(H), wherein U is the matrix of the eigenvectorsof the matrix I_(N)

R_(TX)*, U^(H) is the conjugate transpose of the matrix U and Λ is adiagonal non negative matrix comprising the eigenvalues of the matrixI_(N)

R_(TX)*, and in that the STF linear pre-coding matrix C_(c) is obtainedby multiplying a matrix U′ formed by a part of the columns of the matrixU by the matrix Λ′ which is a diagonal matrix formed by part of thediagonal elements of the matrix Λ.

Thus, through the Kronecker product, the time and/or frequency dimensionis included in the channel description.

According to a particular feature, the matrix Λ′ is formed by selectingthe Q largest non zero diagonal values of the matrix Λ, wherein Q is thenumber of symbols comprised within the vector comprising symbols and thematrix U′ comprises the Q columns of the matrix U associated with the Qlargest values selected for the matrix Λ′.

According to a particular feature, the number Q of symbols comprisedwithin the vector comprising symbols is not divisible by the dimensionN.

According to a particular feature, the STF linear pre-coding matrixC_(c) is calculated from a third matrix V^(H), the matrix V^(H) beingthe transpose conjugate of a unitary matrix V of dimension Q.

According to a particular feature, the matrix V is a Discrete FourierTransform matrix or the matrix V is an Hadamard matrix of dimension Qwhen Q is a power of two.

According to a particular feature, the STF linear pre-coding matrix isC_(c) is calculated using the following formula:C _(c) =αU′Λ′ ^(−1/4) V ^(H),

wherein α=√{square root over (P/Tr(Λ′^(−1/2)))} and P is a predeterminedvalue of average transmit power.

According to still another aspect, the present invention concerns amethod for decoding symbols by a receiver provided with at least onereceiving antenna, the symbols being transmitted by at a transmitterprovided with at least two transmitting antennas through at least achannel in a telecommunication system, the method including a decodingstep wherein a vector comprising received symbols is multiplied by adecoding matrix for producing decoded symbols, characterised in that thedecoding matrix is calculated from an eigenvalue decomposition of amatrix obtained by calculating at least the Kronecker product of theidentity matrix of size N, N being the time and/or the frequencydimension of the code and a matrix obtained from an estimatedcorrelation matrix of the response of the channel.

According to still another aspect, the present invention concerns adevice for decoding symbols being transmitted by one transmitterprovided with at least two transmitting antennas through at least achannel in a telecommunication system, the device comprising decodingmeans wherein a vector comprising received symbols is multiplied by adecoding matrix for producing decoded symbols, characterised in that thedevice comprises means for calculating a decoding matrix from aneigenvalue decomposition of a matrix obtained by calculating at leastthe Kronecker product of the identity matrix of size N, N being the timeand/or the frequency dimension of the code and a matrix obtained from anestimated correlation matrix of the response of the channel.

According to still another aspect, the present invention concerns acomputer program which can be directly loadable into a programmabledevice, comprising instructions or portions of code for implementing thesteps of the method according to the invention, when said computerprogram is executed on a programmable device. Since the features andadvantages relating to the computer program are the same as those setout above relating to the method and device according to the invention,they will not be repeated here.

The characteristics of the invention will emerge more clearly from areading of the following description of an example embodiment, the saiddescription being produced with reference to the accompanying drawings,among which:

FIG. 1 represents a telecommunication system according to the invention;

FIG. 2 represents the calculation module which calculates the STF Codeaccording to the first aspect of the invention or the linear STFpre-coding matrix according to the second aspect of the invention;

FIG. 3 represents the algorithm executed by the calculation moduleaccording the first aspect of the invention;

FIG. 4 represents the algorithm executed by the calculation moduleaccording the second aspect of the invention.

FIG. 1 represents a telecommunication system according to the invention.

The FIG. 1 discloses two communication devices 10 and 20 which exchangeinformation through a wireless MIMO communication channel of thetelecommunication network 150.

The communication device 10 is preferably a base station which transfersto the communication device 20, which is preferably a mobile terminal,data through a MIMO downlink transmission channel of a telecommunicationnetwork 150.

For the sake of simplicity, only one mobile terminal 20 is shown inFIG. 1. Naturally a more important number of mobile terminals receive ortransmit data from or to the base station 10 in the telecommunicationnetwork 150 wherein the present invention is used.

The base station 10 has a plurality of N_(t) antennas respectively notedAntt 1, Antt 2 . . . and Antt N_(t) in the FIG. 1 and the mobileterminal 20 has at least one antenna. As example, the mobile terminalhas a plurality of N_(r) antennas respectively noted Antr 1, Antr 2 toAntr N_(r) creating then a MIMO downlink transmission channel with N_(t)transmit antennas and N_(r) receive antennas.

Preferably and for the sake of simplicity, the transmission of data usesan Orthogonal Frequency Division Multiplexing (OFDM) modulation withN_(c) modulated sub-carriers, each sub-carrier experiences a MIMO flatfading channel, provided that the OFDM parameters are well chosen inparticular with respect to the channel delay spread. The methoddescribed in the present invention can be extended to single carriersystems experiencing inter symbol interferences. In that case, the flatfading MIMO channel to be considered is the delay domain equalizedchannel.

The modulated symbols are transmitted over the space, time and frequencydimensions using a Space-Time-Frequency (STF) block code or a linear STFpre-coder of dimensions N_(t)*N_(time)*N_(freq), wherein N_(time) is thetime dimension of the code in terms of OFDM symbols and N_(freq) is thefrequency dimension of the code in terms of subcarriers. Thus,N=N_(time)*N_(freq) equivalently represents the time dimension for aSpace Time (ST) code or a linear ST pre-coder, the frequency dimensionfor a Space Frequency (SF) code or a linear SF pre-coder and a mix ofboth for a Space Time Frequency (STF) code or a linear STF pre-coder. Asit has been already mentioned, STF, ST, SF codes are considered in thepresent invention as STF codes.

It has to be noted here that if N_(freq)=1, N refers to the particularcase of Space Time coding and if N_(time)=1, N designates the particularcase of Space Frequency coding.

The mobile station 20 implements, according to the invention, a MinimumMean Square Error receiver which estimates the signal encoded by the STFcode according to a first aspect of the invention, or a Minimum MeanSquare Error receiver which estimates the signal pre-encoded by thelinear STF pre-coder at the base station 10 according to the secondaspect of the invention.

The mobile station 20 comprises a channel estimation module 122 thatestimates the instantaneous channel response used by the MMSE receiver.The mobile station 20 comprises also a correlation matrix estimator 120which estimates, from several realisations of the instantaneous channelresponse used by the MMSE receiver, a correlation matrix of the responseof the channel noted R_(TX).

More precisely, the correlation matrix of the response of the channelR_(TX) is an estimation of the transmit correlation matrix of the MIMOchannel of the telecommunication network 150.

The transmit correlation matrix R_(TX) of the MIMO channel of thetelecommunication network 150 is transmitted by the mobile station 20 tothe base station 10 through an uplink MIMO channel of thetelecommunication network 150.

The mobile station 20 comprises also a code determination module 121which determines the code used by the base station 10 according to thecorrelation matrix R_(TX) of the MIMO channel of the telecommunicationnetwork 150.

The mobile station 20 needs also to know at least a part of the STFcoder or of the linear STF pre-coder used by the base station 10 inorder to perform the decoding. The mobile station 20 computes thedecoding matrix to be used as the base station 10 computes the codingmatrix to be used from the knowledge of the estimated correlation matrixR_(TX).

The computed matrix is transferred to the decoding module 123 of themobile station 20 in order to decode the received symbols into estimatedsymbols.

In a variant of realisation, instead of transferring the transmitcorrelation matrix R_(TX) of the MIMO channel of the telecommunicationnetwork 150 to the base station 10, the mobile station 20 transfers thecoding matrix elements to the base station 10 through the uplink MIMOchannel of the telecommunication network 150.

In another variant of realisation, the base station 10 determines thecoding matrix to be used by the base station 10 according to thereceived correlation matrix and transfers it to the mobile station 20.

The base station 10 comprises at least a coding module 100 and acalculation module 110. The coding module 100 is, according to the firstaspect of the invention, a STF coding module, or a linear STF pre-coder,according to the second aspect of the invention.

The STF coding module 100 forms vectors comprising symbols to betransmitted and multiplies each formed vector by a coding matrix forproducing coded symbols to be transmitted over the MIMO channel.

The calculation module 110 has a long term or no channel knowledge. Itmeans that the calculation module 110 receives from time to time theestimated correlation matrix R_(TX) from the mobile station 20 anddetermines a STF coding matrix {tilde over (C)} according to the firstaspect of the invention, or a STF linear pre-coding matrix C_(c)according the second aspect of the invention, from the receivedestimated correlation matrix R_(TX), that minimizes the average, withrespect to the fast fading process, residual Mean Square Error at thereceiver side after MMSE decoding.

The received estimated correlation matrix R_(TX) is representative ofthe macroscopic environment in the vicinity of the base station. Thereceived estimated correlation matrix R_(TX) is then constant when thechannel variations are restricted to the fast fading process.Considering the link between a base station and a mobile station, theestimated correlation matrix R_(TX) is therefore constant during aperiod that is inversely proportional to the speed of the mobile and theupdate frequency of the estimated correlation matrix R_(TX) shouldtherefore be set accordingly.

In practice, the update period is large in comparison with the typicalelementary transmission duration so that the update of the estimatedcorrelation matrix R_(TX) is inexpensive in term of the requiredfeedback bandwidth and in term of workload for the transmit and thereceiving sides.

In a variant of realisation, the calculation module 110, instead ofreceiving from time to time the estimated correlation matrix R_(TX) fromthe mobile station 20, receives the coding matrix or the linearpre-coding matrix computed by the mobile station 10 through the uplinkchannel of the telecommunication network 150.

The calculation module 110 will be described in detail in reference toFIG. 2.

The theoretical bases of the determination of the STF coding matrix{tilde over (C)} and the STF linear pre-coding matrix C_(c) are nowdisclosed.

The following equation describes the discrete time downlink receivedsignal where the signal of one user is transmitted using a STF code:R′=H′(E _(c) S ^(R) +F _(c) S ^(I))+v′  EQ 1

where v′ is a N_(r)N*1 vector of independently and identicallydistributed AWGN complex samples of variance σ².

For the following, the ensemble of real numbers is noted R and theensemble of complex numbers is noted C.

where R′ is a N_(r)N*1 complex vector made of the column vectors R^(i)of R ε C^(Nr*N) stacked on top of each other, each of size N_(r)*1 andH′ is a block diagonal MIMO channel matrix, where each of the N blockscorresponds to a time index for ST codes, or a frequency index for SFcodes, or a mixed time and frequency index for STF codes:

$\begin{matrix}{{R^{\prime} = \begin{pmatrix}R^{1} \\\vdots \\R^{N}\end{pmatrix}},{H^{\prime} = \begin{pmatrix}H_{1} & \cdots & 0 \\\vdots & ⋰ & \vdots \\0 & \cdots & H_{N}\end{pmatrix}}} & {{EQ}\mspace{20mu} 2}\end{matrix}$

where H_(I) ε C ^(Nr*Nt) is a normalized channel matrix, ie the channelcoefficient H_(ij) between a receive antenna i and a transmit antenna jhas a variance equal to E(|H_(ij)|²)=1 and is centered. The channelsmatrices H_(i) may be more or less correlated for different i, but inany case they are characterised by the same correlation matrix.

where S ε C^(Q*l) is the vector containing the Q modulated symbols, Qbeing the number of symbols per STF codeword. S^(R) is the real partRe(S) of S and S^(I) is the imaginary part Im(S) of S. Each symbol of Shas an average energy equal to 1.

The STF code in equation EQ 1 is described with two complex matricesE_(C) and F_(C), one encoding the real part of S, the other one theimaginary part. Equivalently, the STF code can be described with twoother complex matrices C_(c) and D_(c) encoding respectively S and S*.It has to be noted here that S* denotes the conjugate of the matrix S.

where Ec εC^(NtN*Q), Fc εC^(NtN*Q) are the code matrices thatrespectively encode the real part of S and the imaginary part of S. Ithas to be noted that Ec and Fec fully describe the STF code and describein the most general manner all block STF codes from spatial multiplexingas disclosed in the paper of G. D. Golden, G. J. Foschini, R. A.Valenzuela, P. W. Wolniansky, entitled “Detection Algorithm and InitialLaboratory Results using the V-BLAST Space-Time CommunicationArchitecture”, to true STF codes, such as disclosed in the paper ofAlamouti, “A simple transmitter diversity scheme for wirelesscommunications”.

This gives the following equation, equivalent to EQ 1:R′=H′(C _(c) S+D _(c) S*)+v′  EQ 3

When D_(c) is constrained to 0, the resulting STF code is a linear STFpre-coding. Linear STF pre-coding means that the output of the STFpre-encoding process is a linear operation on the input complex vectorS. In this case equation EQ 3 can be written as:R′=H′C _(c) S+v′

In the case of true STF coding, no restriction is put on the codingmatrices E_(c) and F_(c). It is convenient to rewrite EQ 1 with a linearform:

$\begin{matrix}{R^{\prime} = {{{H^{\prime}\begin{bmatrix}E_{c} & F_{c}\end{bmatrix}}\begin{bmatrix}S^{R} \\S^{I}\end{bmatrix}} + v^{\prime}}} & {{EQ}\mspace{20mu} 4}\end{matrix}$

Rewriting EQ 4 with real matrices, we obtain the equivalent equation:

$\underset{\underset{\overset{\sim}{R}}{︸}}{\begin{bmatrix}R^{\prime\; R} \\R^{\prime\; I}\end{bmatrix}} = {{\underset{\underset{\overset{\sim}{H}}{︸}}{\begin{bmatrix}H^{\prime\; R} & {- H^{\prime\; I}} \\H^{\prime\; I} & H^{\prime\; R}\end{bmatrix}}\underset{\underset{\overset{\sim}{C}}{︸}}{\begin{bmatrix}E_{c}^{R} & F_{c}^{R} \\E_{c}^{I} & F_{c}^{I}\end{bmatrix}}\underset{\underset{\overset{\sim}{S}}{︸}}{\begin{bmatrix}S^{R} \\S^{I}\end{bmatrix}}} + \underset{\underset{\overset{\sim}{v}}{︸}}{\begin{bmatrix}v^{\prime\; R} \\v^{\prime\; I}\end{bmatrix}}}$ where${\overset{\sim}{R} \in R^{2{NrN}*1}},{\overset{\sim}{H} \in R^{2{NrN}*2{NtN}}},{\overset{\sim}{C} \in R^{2{NtN}*2Q}},{\overset{\sim}{S} \in R^{2Q*1}},{\overset{\sim}{v} \in {R^{2{NrN}*1}.}}$

The MIMO transmission channel of the telecommunication network isassumed to be flat fading, it means that the discrete time channelresponse between each pair of transmit and receive antennas is modeledas a complex coefficient (H)_(ij), where i is the receive antenna indexand j is the transmit antenna index. Such hypothesis is well suited toOFDM modulation since each subcarrier indeed experiences flat fading,the channel coefficients are equal to the channel frequency response atthe subcarrier frequency, given by the corresponding sample of the FFTof the channel impulse response between the pair of antennas.

We denote R_(TX) the correlation matrix at the transmitter side and Bits square root, so that B^(H)B=R_(TX)

and thus the channel matrix is modeled as:H(t,f)=G(t,f)B*  EQ 5

where G(t,f) is a normalized independently and identically distributedcomplex centered Gaussian matrix. The distribution of each element ofG(t,f) is (1/√{square root over (2 )})(N(0,1)+jN(0,1).

It has to be noted here that in order to simplify the notations theindexes t and f of H and G are dropped.

Combining EQ 5 and EQ 2, H′ becomes:

$\begin{matrix}{H^{\prime} = \begin{pmatrix}{G_{1}B^{*}} & \cdots & 0 \\\vdots & ⋰ & \vdots \\0 & \cdots & {G_{N}B^{*}}\end{pmatrix}} & {{EQ}\mspace{20mu} 6}\end{matrix}$

The independently and identically distributed complex centered Gaussianmatrices G_(i) may be equal or more or less correlated for differentindexes i.

It has to be noted here that the receiver 20 is assumed to have aperfect instantaneous knowledge of the channel of the telecommunicationnetwork 150, which is, as example, commonly implemented by usingappropriate pilot symbols.

Considering that the receiver 20 comprises an MMSE STF detector whichhas a perfect instantaneous channel knowledge, the STF coding module 100or the linear STF pre-coding module 100 uses a STF code that minimizesthe residual Mean Square Error at the receiver side after detection,averaged over the fast fading process, i.e G_(i) in EQ 6.

According to the first aspect of the invention, we will now focus on thebasic principle of the characterisation of the STF coding matrix for STFcode.

As already disclosed, the received signal can be expressed with a linearequation provided that the processing of the real and imaginary partsare made separately.

$\underset{\underset{\overset{\sim}{R}}{︸}}{\begin{bmatrix}R^{\prime\; R} \\R^{\prime\; I}\end{bmatrix}} = {{\underset{\underset{\overset{\sim}{H}}{︸}}{\begin{bmatrix}H^{\prime\; R} & {- H^{\prime\; I}} \\H^{\prime\; I} & H^{\prime\; R}\end{bmatrix}}\underset{\underset{\overset{\sim}{C}}{︸}}{\begin{bmatrix}E_{c}^{R} & F_{c}^{R} \\E_{c}^{I} & F_{c}^{I}\end{bmatrix}}\underset{\underset{\overset{\sim}{S}}{︸}}{\begin{bmatrix}S^{R} \\S^{I}\end{bmatrix}}} + \underset{\underset{\overset{\sim}{v}}{︸}}{\begin{bmatrix}v^{\prime\; R} \\v^{\prime\; I}\end{bmatrix}}}$

The STF coding matrix {tilde over (C)} is found so as to minimize theaverage residual MSE after MMSE detection, under the transmit powerconstraint Tr({tilde over (C)}{tilde over (C)}^(t))=P. At high signal tonoise ratio, i.e 94 ² is small. {tilde over (C)} is found as.

$\overset{\sim}{C} = {\beta\;{\overset{\sim}{U}\begin{pmatrix}{\overset{\sim}{\Lambda}}_{2Q}^{\prime - {1/4}} \\0\end{pmatrix}}V^{\prime\; t}}$

where {tilde over (Λ)}′_(2Q) is a diagonal matrix made of the 2Qstrongest eigenvalues of {tilde over (B)}^(t){tilde over (B)}′and Ũ ismade of the related 2Q eigenvectors followed by arbitrary 2NtN−2Q columnvectors.

${\overset{\sim}{B}\mspace{14mu}{is}\mspace{14mu}{given}\mspace{14mu}{by}\mspace{14mu}\overset{\sim}{B}} = \begin{pmatrix}{I_{N} \otimes B^{R}} & {I_{N} \otimes B^{I}} \\{{- I_{N}} \otimes B^{I}} & {I_{N} \otimes B^{R}}\end{pmatrix}$

where B is a square root of the transmit correlation matrix:B^(H)B=R_(Tx), B^(R)=Re(B) and B^(I)=Im(B). The constant β serves tosatisfy the transmit power constraint. For instance, β is given by:β=√{square root over (P/Tr({tilde over (Λ)}′_(2Q) ^(−1/2)))} for a powerconstraint of P.

Similarly, {tilde over (C)} can be written as:

{tilde over (C)}=βŨ′{tilde over (Λ)}′_(2Q) ^(−1/4)V′^(t) where Ũ′ is a2N_(t)N*2Q matrix made of the first 2Q columns of Ũ.

It has to be noted here that all the involved matrices here are realmatrices and that V′ is only required to be an orthonormal 2Q*2Q matrix.

According to a preferred mode of realisation, the matrix V′^(t) is atranspose matrix of a matrix V′ which can be refined so as to maximizethe minimum average residual SINR per detected real dimension after MMSEequalization. V′ can be chosen as a Hadamard matrix of dimension 2Q when2Q is a power of 2.

V′^(t) can also be obtained from a Discrete Fourier Transform matrix Fusing the following formula:

$V^{\prime\; t} = \begin{pmatrix}F^{R^{t}} & {- F^{I^{t}}} \\F^{I^{t}} & F^{R^{t}}\end{pmatrix}$where F^(Rt) is the transpose of the real part of the matrix F andF^(It) is the transpose of the imaginary part of the matrix F.

According to the second aspect of the invention, we will now focus onthe basic principle of the characterisation of the STF linear pre-codingmatrix.

Starting with equation EQ 3 where Dc is set to zero, we consider thatthe receiver implements an MMSE STF detector, we assume that perfectinstantaneous channel knowledge is available at the receiver side.

The coding matrix C_(c) is found so as to minimize the average residualMSE after MMSE detection, under the transmit power constraintTr(C_(c)C_(c) ^(t))=P.

We use the Eigen Value Decomposition (EVD) of R_(TX)*:R_(TX)*=UΛU^(H).

The EVD of I_(N){circumflex over (x)}R_(Tx)* is then given by:

${I_{N} \otimes R_{Tx}^{*}} = {\underset{\underset{U^{\prime}}{︸}}{\left( {I_{N} \otimes U} \right)}\underset{\underset{\Lambda^{\prime}}{︸}}{\left( {I_{N} \otimes \Lambda} \right)}\underset{\underset{U^{\prime\; H}}{︸}}{\left( {I_{N} \otimes U^{H}} \right)}}$

At high signal to noise ratio, C_(c) is found as:

$\begin{matrix}{C_{c} = {\alpha\;{U^{\prime}\begin{pmatrix}\Lambda_{Q}^{\prime - {1\text{/}4}} \\0\end{pmatrix}}V^{H}}} & {{EQ}\mspace{14mu} 7}\end{matrix}$

where Λ′_(Q) is a diagonal Q*Q matrix made of the Q largest eigenvaluesof I_(N)

Λ, the first Q column vectors of U′ are made of the Q column vectors ofI_(N)

U associated with the eigenvalues of 79 _(Q)′. The remaining N_(t)N−Qcolumn vectors of U′ have no importance as they are not used. So theircan be set to zero or to any arbitrary value.

α is a normalization coefficient that is used to satisfy the transmitpower constraint. For instance α=√{square root over (P/Tr(Λ′_(Q)^(−1/2)))} for a constraint of transmit power P.

Similarly, C_(c) can be written asC _(c) =αU″Λ′ _(Q) ^(−1/4) V ^(H)

Where U″ is a N_(t)N*Q matrix made of the first Q columns of U′.

In EQ 7, U′, a and Λ′_(Q) are fully defined, V is only required to beunitary. However, whereas any unitary matrix V gives the same averagevalue of the MSE with respect to the fast fading process, the choice ofV influences the resulting Bit Error Rate (BER).

According to a preferred embodiment, V can be determined so as tomaximize the minimum average signal to noise plus interference ratiodenoted SINR per dimension of the detected signal. Discrete Fouriermatrices and Hadamard matrices are found to be local optima of thisproblem.

Thus, V can be chosen, according to a particular feature as a DiscreteFourier Transform or a Hadamard matrix of dimension Q.

In the case of Hadamard matrices, Q needs to be a power of two.

According to a variant, V can be chosen as a unitary linear precodingmatrix such as described by S. Galliou, J. C. Belfiore in “Une nouvellefamille de codes espace-temps linéaires, de rendement et de diversitémaximaux”, Proc. Propagation Electromagnétique dans l'Atmosphère duDécamétrique à l'Angström, Rennes 13, 14, 15 Mars 2002, pp. 117-118 orby N. Gresset, J. Boutros, L. Brunel in “Optimal linear precoding forBICM over MIMO channels,” Proc. of the IEEE International Symposium onInformation Theory, Chicago, p. 66, June 2004.

FIG. 2 represents the calculation module which calculates the STF Codeaccording to the first aspect of the invention or the STF linearpre-coding matrix according to the second aspect of the invention.

The calculation module 110 has an architecture based on componentsconnected together by a bus 201 and a processor 202 controlled by aprogram as disclosed in FIG. 3. The calculation module 110 can beintegrated in one or several integrated circuits.

The calculation module 110 comprises memory means 203 made by at leastone random access memory and a non-volatile memory.

The bus 201 links the processor 202 to the memory means 203, theinterface ANT I/F 206 which receives the estimated correlation matrixR_(TX) or the conjugate of the estimated correlation matrix R*_(TX) fromthe mobile station 20 and the interface cod I/F 207 which enables thetransfer to the STF coding module 100 of the calculated STF linearpre-coding matrix C_(c) or the STF coding matrix {tilde over (C)}according to the obtained correlation matrix R_(TX).

The random access memory contains registers intended to receivevariables, digital data and intermediate processing values. Thenon-volatile memory stores the program which enables the module and, inparticular, the processor 202, to operate. The processor 202 controlsthe operation of the principal components of the calculation module 110.

FIG. 3 represents the algorithm executed by the calculation moduleaccording the first aspect of the invention.

The code of this flow chart is for example stored in a non volatilememory of the memory 203 of the calculation module 110. Regularly, at afrequency that depends on the mobile station maximum Doppler Frequency,which typically corresponds to a refreshing period of a few hundreds ofmilliseconds at the carrier frequency of 5 GHz and a mobile stationspeed of 3 meters per second, the calculation module 110 executes theinstructions associated to the algorithm described in the FIG. 3.

At step S300 the calculation module 110 obtains the estimatedcorrelation matrix R_(TX). The estimated correlation matrix R_(TX), isreceived through the uplink MIMO channel of the telecommunicationnetwork 150 and from the correlation matrix estimator 120 of the mobilestation 20. The estimated correlation matrix is then stored in therandom access memory of the memory 203.

It has to be noted here that the correlation matrix R_(TX) can be alsoestimated by the calculation module 110 when the uplink channels areconsidered to have long term statistics equal to the long termstatistics of the downlink channels.

At next step S301, the processor 202 calculates the matrix {tilde over(R)}_(Tx)* using the following formula:

${\overset{\sim}{R}}_{TX}^{*} = \begin{pmatrix}I_{N} & {\otimes R_{TX}^{R}} & I_{N} & {\otimes R_{TX}^{I}} \\{- I_{N}} & {\otimes R_{TX}^{I}} & I_{N} & {\otimes R_{TX}^{R}}\end{pmatrix}$where R_(TX) ^(R) is the real part of the matrix R_(TX) and R_(TX) ^(I)is the imaginary part of the matrix R_(TX.)

Through the Kronecker product, the time and/or frequency dimension isincluded in the channel description, so that the coding solution is aSTF code. It has space and a time and/or a frequency dimension.

At next step S302 the processor 202 executes an eigenvalue decompositionnoted EVD of the matrix {tilde over (R)}_(TX)*. The matrix {tilde over(R)}_(TX)* is then decomposed in {tilde over (R)}_(TX)*=Ũ{tilde over(Λ)}Ũ′ wherein Ũ is the matrix of the eigenvectors of the matrix {tildeover (R)}_(TX)*, Ũ′ is the transpose of the matrix Ũ and {tilde over(Λ)} is a non negative diagonal matrix comprising the eigenvalues of thematrix {tilde over (R)}_(TX)*.

At next step S303, the processor 203 reorders the eigenvalues of thematrix {tilde over (Λ)} according to a predetermined criterion,preferably from the highest value to the lowest one. The processor 202reorders the column vectors of Ũ accordingly and the line vectors of Ũ′accordingly.

At next step S304, the processor 202 forms a matrix {tilde over (Λ)}′which is a diagonal matrix made of the 2Q strongest eigenvalues of{tilde over (R)}_(TX)*.

At next step S305, the processor 202 forms a matrix Ũ′ which is made ofthe related 2Q eigenvectors of the strongest eigenvalues followed byarbitrary 2N_(t)N−2Q column vectors.

At next step S306, the processor 202 obtains the matrix V′ as definedpreviously.

At next step S307, the processor 202 calculates the factor β using thefollowing formula:β=√{square root over (P/Tr({tilde over (Λ)}′_(2Q) ^(−1/2)))}where P is the desired average transmit power.

At next step S308, the processor 202 calculates the STF coding matrix{tilde over (C)} using the following formula:{tilde over (C)}=βŨ′{tilde over (Λ)}′ ^(−1/4) V′ ^(T)

At next step S309, the STF coding matrix {tilde over (C)} is transferredto the STF coding module 100.

A next step S310, vectors of a dimension of 2Q are formed. Each vectorcomprises the real parts and the imaginary parts of the symbols to betransmitted which are stacked on top of each other. Each formed vectoris multiplied by the STF coding matrix {tilde over (C)} for producingcoded symbols to be transferred.

It has to be noted here that, according to a particular feature, thecode determination module 121 of the mobile station 20 executes thepresent algorithm in a similar way as the one disclosed here in order tocalculate the STF coding matrix Caused by the decoding module 123 of themobile station 20. In such case, the received symbols a group intovectors of dimension 2Q which are each multiplied by the STF decodingmatrix calculated from an eigenvalue decomposition of a matrix obtainedby calculating at least the Kronecker product of the identity matrix ofsize N for producing estimated symbols.

It has to be noted here that, according to a variant, the STF codingmatrix {tilde over (C)} is transferred to the code determination module121 of the mobile station 20.

According to a particular feature, {tilde over (C)} is computed by thecode determination module 121 and transferred by the mobile station 20to the base station 10.

FIG. 4 represents the algorithm executed by the calculation moduleaccording the second aspect of the invention.

The code of this flow chart is for example stored in a non volatilememory of the memory 203 of the calculation module 110. Regularly, at afrequency that depends on the mobile station maximum Doppler Frequency,the calculation module 110 executes the instructions associated to thealgorithm described in the FIG. 4.

At step S400 the calculation module 110 obtains the conjugate of theestimated correlation matrix {tilde over (R)}*_(TX). The estimatedcorrelation matrix R_(TX) is received through the uplink MIMO channel ofthe telecommunication network 150 and from the correlation matrixestimator 120 of the mobile station 20. The estimated correlation matrixis then stored in the random access memory of the memory 203.

It has to be noted here that the conjugate of the correlation matrix{tilde over (R)}*_(TX) can be also estimated by the calculation module110 when the uplink channels are considered to have long term statisticsequal to the long term statistics of the downlink channels.

At next step S401, the processor 202 calculates an eigenvaluedecomposition noted EVD of the conjugate of the estimated correlationmatrix {tilde over (R)}*_(TX). {tilde over (R)}*_(TX) is then decomposedin {tilde over (R)}_(TX)*=UΛU^(H).

Wherein U is the matrix of the eigenvectors of the conjugate of theestimated correlation matrix {tilde over (R)}_(TX)*, U^(H) is theconjugate transpose of the matrix U and Λ is the matrix of theeigenvalues of the conjugate of the estimated correlation matrix {tildeover (R)}*_(TX).

At next step S402, the processor 202 calculates the Kronecker product ofthe identity Matrix I_(N) of dimension N and the matrix U. The resultingmatrix is noted the matrix U′.

At next step S403, the processor 202 calculates the Kronecker product ofthe identity Matrix I_(N) and the matrix Λ. The resulting matrix iscalled the matrix Λ′ which is a diagonal matrix comprising theeigenvalues.

At next step S404, the processor 202 calculates the Kronecker product ofthe identity Matrix I_(N) and the matrix U^(H). The resulting matrix iscalled the matrix U′^(H).

Through the Kronecker product, the time and/or frequency dimension isincluded in the channel description, so that the coding solution is atrue linear STF pre-coding. It has space and a time and/or a frequencydimension.

At next step S405, the processor 202 reorders the eigenvalues of thematrix Λ′ according to a predetermined criterion, preferably from thehighest values to the lowest one. The processor 202 reorders the columnvectors of U′ accordingly and the line vectors of U′^(H) accordingly.

At next step S406, the processor 202 forms a matrix Λ′_(Q) which is adiagonal matrix made of the Q strongest eigenvalues of Λ′.

At next step S407, the processor 202 obtains the matrix V^(H) as definedpreviously.

At next step S408, the processor 202 calculates the STF linearpre-coding matrix C_(c) using the following formula:C _(c) =αU′Λ ^(′−1/4) V ^(H),wherein α=√{square root over (P/Tr(Λ′^(−1/2)))} and P is a predeterminedvalue of power.

At next step S409, the STF linear pre-coding matrix C_(c) is transferredto the STF pre-coding module 100.

The symbols to be transmitted are grouped into vectors of Q complexelements. Each vector of dimension Q is multiplied by the STF codingmatrix C_(c) at step S410.

It has to be noted here that the code determination module 121 of themobile station 20 executes the present algorithm in a similar way as theone disclosed here in order to calculate the STF linear pre-codingmatrix C_(c) used by the decoding module 123 of the mobile station 20.In such case, the received symbols a group into symbols of dimension Qwhich are each multiplied by the STF linear decoding matrix calculatedfrom an eigenvalue decomposition of a matrix obtained by calculating atleast the Kronecker product of the identity matrix of size N forproducing estimated symbols.

According to a particular feature, C_(c) is computed by the codedetermination module 121 and transferred by the mobile station 20 to thebase station 10.

It has to be noted here that, according to a variant, the STF linearpre-coding matrix C_(c) is transferred to the code determination module121 of the mobile station 20.

Naturally, many modifications can be made to the embodiments of theinvention described above without departing from the scope of thepresent invention.

1. A method for transmitting symbols through at least one channel in atelecommunication system including at least one transmitter providedwith at least two transmitting antennas and at least one receiverprovided with at least one receiving antenna, the method comprising:obtaining an intermediate matrix by calculating at least a Kroneckerproduct of an identity matrix of size N, where the size N is a timeand/or a frequency dimension of a code, and an estimated correlationmatrix of a response of the at least one channel established between thetransmitter and the receiver; calculating a coding matrix from aneigenvalue decomposition of the intermediate matrix; and encodingaccording to the code to produce coded symbols to be transmitted overthe at least one channel established between the transmitter and thereceiver by multiplying a vector comprising the symbols by the codingmatrix.
 2. The method according to claim 1, wherein the coding matrix{tilde over (C)} is calculated from the eigenvalue decomposition of theintermediate matrix {tilde over (R)}*_(TX) being obtained by calculatingthe Kronecker product of the identity matrix I_(N) of size N and thereal part R_(TX) ^(R) of the estimated correlation matrix of theresponse of the at least one channel and by calculating the Kroneckerproduct of the identity matrix I_(N) of size N and the imaginary partR_(TX) ¹ of the estimated correlation matrix of the response of the atleast one channel.
 3. The method according to claim 2, wherein theintermediate matrix {tilde over (R)}*_(TX) is equal to:${{\overset{\sim}{R}}_{Tx}^{*} = \begin{pmatrix}I_{N} & {\otimes R_{Tx}^{R}} & I_{N} & {\otimes R_{Tx}^{I}} \\{- I_{N}} & {\otimes R_{Tx}^{I}} & I_{N} & {\otimes R_{Tx}^{R}}\end{pmatrix}},$ wherein

is the Kronecker product.
 4. The method according to claim 3, whereinthe eigenvalue decomposition of the matrix {tilde over (R)}*_(TX) isequal to Ũ{tilde over (Λ)}Ũ′, wherein Ũ is a matrix of eigenvectors ofthe matrix {tilde over (R)}*_(TX), Ũ′ is a transpose of the matrix Ũ and{tilde over (Λ)} is a diagonal non negative matrix comprisingeigenvalues of the intermediate matrix {tilde over (R)}*_(TX), and inthat the coding matrix {tilde over (C)} is obtained by multiplying thematrix Ũ′ formed by a part of the columns of the matrix Ũ by a diagonalmatrix {tilde over (Λ)}′ formed by a part of the diagonal matrix {tildeover (Λ)}.
 5. The method according to claim 4, wherein the matrix {tildeover (Λ)}′ is formed by selecting the 2*Q largest non zero diagonalvalues of the matrix {tilde over (Λ)}, wherein Q is a number of symbolscomprised within the vector comprising the symbols and the matrix Ũ′comprises the 2*Q columns of the matrix Ũ associated, in the same order,with the 2*Q largest values selected from the matrix {tilde over (Λ)}′.6. The method according to claim 5, wherein the number Q of symbolswithin the vector comprising the symbols is not divisible by the sizeN′.
 7. The method according to claim 6, wherein the coding matrix {tildeover (C)} is calculated from a matrix V′^(t), the matrix V′^(t) beingthe transpose of an orthonormal matrix V′ of dimension 2*Q.
 8. Themethod according to claim 7, wherein the matrix V′ is obtained from aDiscrete Fourier Transform matrix.
 9. The method according to claim 7,wherein the matrix V′ is an Hadamard matrix of dimension 2*Q when 2*Q isa power of two.
 10. The method according to claim 7, wherein the codingmatrix {tilde over (C)} is calculated using the following formula:{tilde over (C)}=βŨ′Ã{tilde over ( )}′ ^(−1/4) V′ ^(t) whereinβ=√{square root over (P/Tr({tilde over (Λ)}′^(−1/2)))} for apredetermined average transmit power of P, where Tr is a traceoperation.
 11. The method according to claim 1, wherein the codingmatrix is a Space-Time Frequency (STF) linear pre-coding matrix C_(c)and the intermediate matrix obtained from the estimated correlationmatrix of the response of the at least one channel R*_(TX) is theconjugate matrix of the estimated correlation matrix R_(TX) of thefrequency response of the channel.
 12. The method according to claim 11,wherein the eigenvalue decomposition of a matrix I_(N)

R*_(TX) is equal to UΛU^(H), wherein I_(N) is the identity matrix,

is the Kronecker product, U is a matrix of eigenvectors of the matrixI_(N)

R*_(TX), U^(H) is a conjugate transpose of the matrix U and Λ is a nonnegative diagonal matrix comprising eigenvalues of the matrix I_(N)

R*_(TX), and in that the STF linear pre-coding matrix C_(c) is obtainedby multiplying a matrix U′ formed by a part of the columns of the matrixU by the matrix Λ′ which is a diagonal matrix formed by part of thediagonal elements of the matrix Λ.
 13. The method according to claim 12,wherein the matrix Λ′ is formed by selecting the Q largest non zerodiagonal values of the matrix Λ, wherein Q is a number of symbolscomprised within the vector the comprising symbols and the matrix U′comprises the Q columns of the matrix U associated with the Q largestvalues selected for the matrix Λ′.
 14. The method according to claim 13,wherein the number Q of symbols within the vector comprising the symbolsis not divisible by the size N.
 15. The method according to claim 14,wherein the STF linear pre-coding matrix C_(c) is calculated from amatrix V^(H), the matrix V^(H) being the transpose conjugate of aunitary matrix V of dimension Q.
 16. The method according to claim 15,wherein the unitary matrix V is a Discrete Fourier Transform matrix. 17.The method according to claim 15, wherein the matrix V is an Hadamardmatrix of dimension Q when Q is a power of two.
 18. The method accordingto claim 15, wherein the STF linear pre-coding matrix C_(c) iscalculated using the following formula:C _(c)=αU′Λ′^(−1/4) V ^(H), wherein α=√{square root over(P/Tr(Λ′^(−1/2)))}, Tr is a trace operation and P is a predeterminedvalue of average transmit power.
 19. A device for transmitting symbolsthrough at least one channel in a telecommunication system including atleast one transmitter provided with at least two transmitting antennasand at least one receiver provided with at least one receiving antenna,the device comprising: an obtaining section configured to obtain anintermediate matrix by calculating at least a Kronecker product of anidentity matrix of size N, where the size N is a time and/or a frequencydimension of a code, and an estimated correlation matrix of a responseof the at least one channel established between the transmitter and thereceiver; a calculating section configured to calculate a coding matrixfrom an eigenvalue decomposition of the intermediate matrix; and anencoding section configured to produce coded symbols according to thecode to be transmitted over the at least one channel established betweenthe transmitter and the receiver by multiplying a vector comprising thesymbols by the coding matrix.
 20. A method for decoding symbols receivedby a receiver provided with at least one receiving antenna, the symbolsbeing transmitted by a transmitter provided with at least twotransmitting antennas through at least one channel in atelecommunication system, the method comprising: obtaining anintermediate matrix by calculating at least a Kronecker product of anidentity matrix of size N, where the size N is a time and/or a frequencydimension of a code, and an estimated correlation matrix of a responseof the at least one channel established between the transmitter and thereceiver; calculating a decoding matrix from an eigenvalue decompositionof the intermediate matrix; and decoding, according to the code, toproduce decoded symbols by multiplying the received symbols received bythe receiver over the at least one channel by the decoding matrix.
 21. Adevice for decoding symbols received by a receiver provided with atleast one receiving antenna, the symbols being transmitted by onetransmitter provided with at least two transmitting antennas through atleast one channel in a telecommunication system, the device comprising:an obtaining section configured to obtain an intermediate matrix bycalculating at least a Kronecker product of an identity matrix of sizeN, where the size N is a time and/or a frequency dimension of a code,and an estimated correlation matrix of a response of the at least onechannel established between the transmitter and the receiver; acalculating section configured to calculate a decoding matrix from aneigenvalue decomposition of the intermediate matrix; and a decodingsection configured to produce decoded symbols according to the code bymultiplying received symbols received from the transmitter over the atleast one channel by the decoding matrix.
 22. A computer readable mediumstoring instructions executable by a processor to perform a method fortransmitting symbols through at least one channel in a telecommunicationsystem including at least one transmitter provided with at least twotransmitting antennas and at least one receiver provided with at leastone receiving antenna, the method comprising: obtaining an intermediatematrix by calculating at least a Kronecker product of an identity matrixof size N, where the size N is a time and/or a frequency dimension of acode, and an estimated correlation matrix of a response of the at leastone channel established between the transmitter and the receiver;calculating a coding matrix from an eigenvalue decomposition of theintermediate matrix; and encoding, according to the code, to producecoded symbols to be transmitted over the at least one channelestablished between the transmitter and the receiver by multiplying avector comprising the symbols by the coding matrix.
 23. A computerreadable medium storing instructions executable by a processor toperform a method for decoding symbols received by a receiver providedwith at least one receiving antenna, the symbols being transmitted by atransmitter provided with at least two transmitting antennas through atleast one channel in a telecommunication system, the method comprising:obtaining an intermediate matrix by calculating at least a Kroneckerproduct of an identity matrix of size N, where the size N is a timeand/or a frequency dimension of a code, and an estimated correlationmatrix of a response of the at least one channel established between thetransmitter and the receiver; calculating a decoding matrix from aneigenvalue decomposition of the intermediate matrix; and decoding,according to the code, to produce decoded symbols by multiplying thereceived symbols received by the receiver over the at least one channelby the decoding matrix.